Question

For the following 4 questions, consider the following 10 scores on a test:

45 45 60 65 75 80 85 90 90 100

A) Find the standard deviation of the data (to the nearest hundredth).

B) Calculate the 25^th percentile of the data.

Answer 1

Solution:

x	x2
45	2025
45	2025
60	3600
65	4225
75	5625
80	6400
85	7225
90	8100
90	8100
100	10000
x=735	x2=57325

A ) The sample standard is S

  S =( x2 ) - (( x)2 / n ) n -1

=57325-(735)210/9

=57325-54022.5/9

=3302.59

=366.9444

=19.1558

The sample standard =19.15

B ) Arranging Observations in the ascending order, We get :
45,45,60,65,75,80,85,90,90,100

Here, n=10

P25=(25(n+1)100)th value of the observation

=(25⋅11100)th value of the observation

=(2.75)th value of the observation

=2nd observation +0.75[3rd-2nd]

=45+0.75[60-45]

=45+0.75(15)

=45+11.25

=56.25

P25=56.25